1 ! Copyright (C) 2005, 2010 Slava Pestov, Joe Groff.
2 ! See http://factorcode.org/license.txt for BSD license.
3 USING: accessors arrays columns kernel locals math math.bits
4 math.functions math.order math.vectors sequences
5 sequences.private fry ;
9 : zero-matrix ( m n -- matrix )
10 '[ _ 0 <array> ] replicate ;
12 : identity-matrix ( n -- matrix )
13 #! Make a nxn identity matrix.
14 iota dup [ = 1 0 ? ] cartesian-map ;
16 :: rotation-matrix3 ( axis theta -- matrix )
19 axis first3 :> ( x y z )
20 x sq 1.0 x sq - c * + x y * 1.0 c - * z s * - x z * 1.0 c - * y s * + 3array
21 x y * 1.0 c - * z s * + y sq 1.0 y sq - c * + y z * 1.0 c - * x s * - 3array
22 x z * 1.0 c - * y s * - y z * 1.0 c - * x s * + z sq 1.0 z sq - c * + 3array
25 :: rotation-matrix4 ( axis theta -- matrix )
28 axis first3 :> ( x y z )
29 x sq 1.0 x sq - c * + x y * 1.0 c - * z s * - x z * 1.0 c - * y s * + 0 4array
30 x y * 1.0 c - * z s * + y sq 1.0 y sq - c * + y z * 1.0 c - * x s * - 0 4array
31 x z * 1.0 c - * y s * - y z * 1.0 c - * x s * + z sq 1.0 z sq - c * + 0 4array
32 { 0.0 0.0 0.0 1.0 } 4array ;
34 :: translation-matrix4 ( offset -- matrix )
35 offset first3 :> ( x y z )
43 : >scale-factors ( number/sequence -- x y z )
44 dup number? [ dup dup ] [ first3 ] if ;
46 :: scale-matrix3 ( factors -- matrix )
47 factors >scale-factors :> ( x y z )
54 :: scale-matrix4 ( factors -- matrix )
55 factors >scale-factors :> ( x y z )
63 : ortho-matrix4 ( dim -- matrix )
64 [ recip ] map scale-matrix4 ;
66 :: frustum-matrix4 ( xy-dim near far -- matrix )
67 xy-dim first2 :> ( x y )
70 near far + near far - /f :> zf
71 2 near far * * near far - /f :> wf
80 :: skew-matrix4 ( theta -- matrix )
91 : mneg ( m -- m ) [ vneg ] map ;
93 : n*m ( n m -- m ) [ n*v ] with map ;
94 : m*n ( m n -- m ) [ v*n ] curry map ;
95 : n/m ( n m -- m ) [ n/v ] with map ;
96 : m/n ( m n -- m ) [ v/n ] curry map ;
98 : m+ ( m m -- m ) [ v+ ] 2map ;
99 : m- ( m m -- m ) [ v- ] 2map ;
100 : m* ( m m -- m ) [ v* ] 2map ;
101 : m/ ( m m -- m ) [ v/ ] 2map ;
103 : v.m ( v m -- v ) flip [ v. ] with map ;
104 : m.v ( m v -- v ) [ v. ] curry map ;
105 : m. ( m m -- m ) flip [ swap m.v ] curry map ;
107 : m~ ( m m epsilon -- ? ) [ v~ ] curry 2all? ;
109 : mmin ( m -- n ) [ 1/0. ] dip [ [ min ] each ] each ;
110 : mmax ( m -- n ) [ -1/0. ] dip [ [ max ] each ] each ;
111 : mnorm ( m -- n ) dup mmax abs m/n ;
113 : cross ( vec1 vec2 -- vec3 )
114 [ [ { 1 2 0 } vshuffle ] [ { 2 0 1 } vshuffle ] bi* v* ]
115 [ [ { 2 0 1 } vshuffle ] [ { 1 2 0 } vshuffle ] bi* v* ] 2bi v- ; inline
117 :: normal ( vec1 vec2 vec3 -- vec4 )
118 vec2 vec1 v- vec3 vec1 v- cross normalize ; inline
121 [ [ v. ] [ norm-sq ] bi / ] keep n*v ;
126 : angle-between ( v u -- a )
127 [ normalize ] bi@ v. acos ;
129 : (gram-schmidt) ( v seq -- newseq )
130 [ dupd proj v- ] each ;
132 : gram-schmidt ( seq -- orthogonal )
133 V{ } clone [ over (gram-schmidt) over push ] reduce ;
135 : norm-gram-schmidt ( seq -- orthonormal )
136 gram-schmidt [ normalize ] map ;
139 make-bits over first length identity-matrix
140 [ [ dupd m. ] when [ dup m. ] dip ] reduce nip ;